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For each of the statements below state whether it is True or False. If True then give a proof. If False then explain why, e.g.,

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For each of the statements below state whether it is True or False. If True then give a proof. If False then explain why, e.g., by giving a counterexample. (a) The sum of the squares of any two rational numbers is a rational number. (b) For all positive xR, if x is irrational then x is irrational. (c) For all x,yR, if x and y are irrational then x2+y is irrational. (d) log10(2) is irrational

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